It isn't the color space of the NEF files because NEF files don't have a color space. When the image is opened in Photoshop it has been converted to an RGB image and different color spaces come into play there. So something else is causing havoc with your workflow, but I'm not enough of an expert to tell you what it is.
I open Nikon Raw files whose native space is AdobeRGB into Adobe Camera Raw. ACR has always successfully recognized that the display space for these is Adobe RGB.
That isn't exactly how ACR works. As Jim said, raw files from any camera have no inherent RGB color space because they haven't been converted to RGB yet. When you set a camera to Adobe RGB and shoot raw, the color space you are setting is only for the JPEG preview and in-camera histogram/clipping display of the raw photo, but does not affect the raw photo itself.
The color space ACR uses is set by the Workflow Options dialog box that you open by clicking the underlined blue text at the bottom of the Camera Raw dialog box. If ACR is opening raw files as sRGB, it's because at some point the color space has been switched to sRGB in the Workflow Options dialog box.
There's enough here to correct some of my mistaken beliefs, but if you look at my modified description of the problem, I don't think we've addressed it.
The assigned color space for these images on my camera is Adobe RGB. I understand that for a RAW file, this isn't really "there", but ACR at least notices this preference and brings the image up with the image tagged as Adobe RGB in "Workflow Options". Then when the imiage is brought into Photoshop, it has AdobeRGB as the assigned space. Based on what you are telling me, this process is irrelevant.
The problem is this: the colors shown onscreen in ACR differ from what is seen when the image is brought into Photoshop. (It also differes from Bridge). The difference between to two is similar to the difference between an AdobeRGB image when it is displayed in the correct color space and when it is displayed as sRGB. It doesn't sound like that kind of assignment issue is what is really going on here, but what is true is that colors onscreen in ACR aren't right. Changing the color space in "workflow options" doesn't change the way the colors appear in ACR. What matters is that when the image is opened into Photoshop, the images are far more vibrant (and to my eyes, correct, as the ACR display looks muted and sour).
The bottom line is that something is affecting how ACR displays its colors since the 10.3 update: right now I don't see it as likely being a problem internal to ACR that I could fix by changing a setting, but rather a byproduct of 10.3 interacting with SpectraView or my video card in a way that is different than how Photoshop works with the calibration or the card.
I'm inclined to rebuild my machine from scratch, test the Photoshop and ACR performance before I add monitor calibration. That could rule out that as an influence here. I might also look for another computer that has a different video card.
Fortunately, my 10.2 ACR machine works fine.
Which profile is selected when you open the file in ACR 10.3? Adobe Color?
What happens when you manually select Adobe Standard?
It has already been mentioned, but check again in which color space the image shall be opened in ACR, by clicking on the line looking like a hyperlink, below the image. I believe to remember that the factory default used to be Adobe RGB 1998.